Donald Trump’s powerful stance against trade deals and globalization has just about everybody in the political arena squirming — everybody, that is, except Mr. Trump and the blue-collar supporters he will need to win the White House in November.

His fierce attack on the North American Free Trade Agreement and the pending Trans-Pacific Partnership tradeagreement exposed a gaping rift in the Republican Party that has been plastered over for years between pro-business Republican leaders and the party’s working-class voters.

The usually firmly Republican-allied U.S. Chamber of Commerce was looking for cover Wednesday after clashing with Mr. Trump, the presumptive Republican presidential nominee, over his anti-globalization agenda.

Yet Mr. Trump’s populist rhetoric gave voice to working-class voters, who have often found themselves on the other side of the divide from business leaders and politicians both Republican and Democratic.

“It is a long-standing divide that is only growing bigger because of the role of globalization in the world economy and the U.S. economy,” said Ford O’Connell, a Republican Party strategist and conservative activist.

He said the Chamber might want to get out of the way of the Trump Train in states such as Pennsylvania, where polls show Mr. Toomey leading in the Senate race and Mr. Trump tied with Mrs. Clinton in the presidential race.

“You wonder if the Chamber’s actually catching on to what is taking place here,” he said. “Maybe the Chamber might be better off to back Toomey in private and not be so public about it.”